Continuity is one of the cooler sets of features in OS X Yosemite, but it's limited to newer Macs that support Bluetooth LE. Now, you can easily add that feature to your older Mac with a Bluetooth dongle and a bit of software.
On the software end, you'll need a copy of Continuity Activation Tool installed. Up until recently, this software added support for Continuity to older Macs, but it required you to install a new card into your Mac, and it didn't support USB dongles. From there, you'll just need a Bluetooth 4.0 dongle, preferably one built using the Broadcom BCM20702 chip. With that, you'll be on your way to using most Continuity features, including Handoff and Airdrop.
Continuity Activation Tool [GitHub]